(c)(5 points)Determine an invertible matrixSand a diagonal matrixDsuch thatD=S-1AS. (You do not need to computeS-1!).Solution:D=λ1000λ2000λ3=000020002S=~v1~v2~v3=1-111101012. LetV=span{et, tet, t2et}.You are told that these three functions form a basisBofV. LetT:V-→Vbe given byT(f) =f0(t)-f(t).(a)(7 points)Find a basis for the kernel ofT.(b)(7 points)Find a basis for the image ofT.(c)(7 points)Determine the matrix ofTwith respect to the basisB.

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